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How do I model disturbed zones?

We don't have a particular tutorial that discusses disturbed zones, but in general the idea is to define a zone around your excavation with a disturbed state.

You add the disturbed zone in the stage in which the material is excavated, turn on the Stage Properties option, and turn off the check box for resetting the stresses. You can reset the yield flag as well. This is like putting in a brand new material but with a lower strength. The material will start off with the stress state from the stronger original material. See the image below.

You do not apply the disturbance factor to the entire rock mass. The disturbance factor, D, should only apply to a limited zone of damaged rock around an excavation or behind a slope face.

For guidance of choosing an appropriate D factor, see Chapter 11: Rock Mass Properties from Hoek's Practical Rock Engineering.

When modeling a coal mine, is it possible to limit the slot convergence?

When modeling a thin slot in RS2, it is certainly possible that you can get convergence greater than the thickness of the slot. There is nothing in RS2 to limit the amount of deformation based on some predefined condition. Obviously, if you find that the deformation exceeds the thickness, this indicates that the excavation is unstable and would close without some sort of support. This assumes all the properties you've defined are realistic. The factors that influence the amount of displacement are 1) strength parameters (if you are getting a lot of failure, then most of the displacement is plastic displacement), and 2) the modulus of the material. You should always make sure that these are correct.

With regards to limiting the slot convergence, this is not an easy thing to do in RS2, and we do not have anything built into the program to handle this. Boundaries are allowed to deform without restriction and there is no way to define a maximum amount of relative displacement between two points.

However, you can try to approximate this with sliding gap liner elements and staging the stress field using the induced stress option.

Sliding gap liner elements are liner elements that do not allow any axial or moment until a certain amount of strain has occurred. So, if you use them as struts between the roof and floor and then define a strain of 100%, basically they’ll kick in once the floor meets the roof. If you then set the modulus of these liners to an extremely high number ( 1e10), then no relative movement will occur between the roof and the floor once they kick in.

Now it’s not a simple matter of adding these liners and doing a quick 1 or 2 stage model. What you have to do is relax the boundary and allow it to displace over a number of stages. This allows the sliding gap elements to properly lock at a certain amount of strain.

Sample models can be downloaded here. The slot in the attached model is 2m high. An unsupported displacement of 3.5m occurs at the center of the excavation. You’ll notice that after the sliding gap elements are added, the roof and floor displacements are around 1m at the center, for a total of 2m convergence. Notice also how the liners pick up the load from the center outwards as the roof and floor meet from stage to stage.

Comparison of supported and unsupported slot excavations in RS2
Comparison of supported and unsupported slot excavations in RS2

Can I use the pseudo-static seismic load capabilities for excavations?

The primary application is in slope stability.

Numerous examples can be found in the Slope Stability Verification Manual in the Verification section of the Online Help.

While the seismic load option is primarily for slope stability applications, the following comments from Evert Hoek regarding seismic loading of tunnels may be of interest:

There are indeed ways of estimating seismic effects on tunnels and probably the best known US author on this is C.H. Dowding (Dowding, C.H., and Rozen, A., ‘Damage to Rock Tunnels from Earthquake Shaking’, Journal of Geotechnical Engineering Division, ASCE, Vol. 104, No. GT2, Febr. 1978.)

A quick search online should result in a few case histories of tunnel problems related to earthquakes.

Do you have any recommendations for modelling a powerhouse cavern excavation?

With regards to cavern excavation, the following discussion is courtesy of Evert Hoek (you can download the attachment here):

I have attached a note on cavern design using Phase2 which may be of assistance to you. Generally, I recommend ignoring the shotcrete lining for a large cavern design and relying on rock bolts or cables to provide the principal support. The shotcrete is applied to protect the rock surface and to bridge the gap between the rockbolt of cable heads but, unless the blasting is perfect, it is very difficult to form a load-bearing shell with a thin shotcrete lining.

You will also find a chapter on large cavern design at

Tunneling & Support

How can I see exactly what liner layer fails?

An RS2 file with the extension .fez is just a zip file. You can unzip the file and the liner results are written in the file with the extension r0#. Note that to unzip the file, first change the file extension from .fez to .zip.

The liner results are located at the end of the file and the formatting is as follows:

  1. Element number
  2. Number of failed layers (liner element is divided into 100 layers)
  3. Liner formulation approach
  4. Connected node number and its forces

An excerpt from an output file is shown in the figure below. The following information is being displayed:

  1. Element number = 5107
  2. Number of failed layers = 0
  3. Liner formulation approach = Timoshenko Beam
  4. Connected node 1: number, σx, σy, σxy, σz = 40, -3.95, -0.00174, 0.0055, 0
  5. Connected node 2: number, σx, σy, σxy, σz = 40, -3.95, -0.00174, 0.0055, 0

Excerpt from RS2 output file .r01

Excerpt from RS2 output file .r01

Note that you also have to select the Save results in text format option.

What methods can be used to degrade a primary liner?

There are two options that can be used to remove the primary liner.

The first method is to use the Removed option in the Define Composite Properties dialog. This allows you to remove any liner from a composite system. The only problem with this is that the Removed option is relative to the install stage. You need multiple composite liners if you're degrading multiple liners (if you have multiple excavation sequences).

The second method uses stage properties. In this case use plastic liners and set the strength to zero in the stage when the liner is removed. If you want to keep the liners elastic until the removal stage, simply define very large values of compressive strength and tensile strength.

How can I calculate the strain in the concrete tunnel lining?

The approximated axial strain in the liner element can be calculated from the axial stress and the bending moment.

The axial strain equals ε=1/E (σa ± Mc/I), where σa is the axial stress, M is the bending moment, c is the perpendicular distance to the neutral axis, and I is the second moment of area.

Note that the above strain formulation is not valid in the plastic regime. In RS2, the liner is divided into a number of layers. Stresses are assumed to be constant over the layer. If stresses exceed the peak stress they drop down to the residual stress. When plasticity occurs, since the stress is no longer linearly distributed, the strain equation is no longer valid.

How is plasticity in the liner accounted for?

The plasticity in the liner is calculated based on layers. When the stresses in a layer exceed the peak stress, they drop to the residual stress. The procedure follows the same approach that is outlined in the book by Owen, D.R.J. and Hinton, E. (1986):

Owen, D.R.J. and Hinton, E. (1986). Finite Elements in Plasticity: Theory and Practice

RS2 does not output the liner strains to interpret.

Why does the bolt support on my tunnel seem to have little effect on the results?

With respect to using bolts for tunnel support in RS2, the following general comments may be useful in helping you to interpret the analysis results or to determine how your model may need to be modified:

  • If the material in the vicinity of the bolts is elastic, there are small relative displacements between the two ends of the bolts. This results in small strains and small stresses/forces in the bolts. If you look at the axial forces in the bolts and compare these to the stress in the rock mass, it is possible that the load is insignificant, and therefore the bolts may be appearing to have no effect. The bolts are simply not putting significant force back into the system.
  • In order to see changes in deformation due to bolts you need a couple of things. First, strains in the bolt generating a significant force that is placed back into the system. These forces, when compared to the stresses in the rock mass, must be significant. For some tunnels, you may not see a significant influence on displacements due to bolts. This is because of the large difference between the ground stresses and the limited amount of force a bolt can put back into the system.
  • Plasticity of the material around the excavation can create the displacement gradient and resulting strain necessary to induce the load in the bolts necessary to see an effect on displacement. If the material is elastic you rarely see an effect on the displacements.

Are the liner forces in RS2 (Shear Force, Axial Force, Bending Moment) the forces per unit width out of plane or per reinforcement member?

The Support Capacity Graph values are for each individual reinforcement member. These values can be easily exported to Excel from RS2.

Support Capacity Plot
Reinforcement Support Capacity Graphs

If you Graph Liner Data, the values are per meter and represent the values in the beam elements used in the analysis.

The method used to determine the forces and moments in each individual member is described in the following reference:

Carranza-Torres, C., Diederichs, M. (2009) Mechanical analysis of circular liners with particular reference to composite supports. For example, liners consisting of shotcrete and steel sets. Tunnelling and Underground Space Technology. 24(5):506-532

Evert Hoek’s Kersten lecture also deals with the spacing of steel sets.

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